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 Volume 45, Issue 4, 1997
Geophysical Prospecting  Volume 45, Issue 4, 1997
Volume 45, Issue 4, 1997


P‐to‐S conversion for a thin anisotropic zone produced by vertical fracturing[Link]
Authors Steve Kelly, Paul Baltensperger and George A. McMechanPoint‐source synthetic seismic responses for a thin, fractured bed are generated, interpreted and processed. The synthesis is carried out for a compressional source and multicomponent surface receivers. The anisotropy considered has hexagonal symmetry, with a horizontal symmetry axis, and represents oil‐ and gas‐filled, aligned vertical fractures for a broad range of fracture densities and aspect ratios. P‐to‐S reflected conversions recorded on the horizontal geophones show both kinematic and dynamic anomalies that increase with increasing fracture density and are only weakly dependent on aspect ratio. In contrast, the vertical component P‐wave reflections provide a much poorer diagnostic of fracturing. Analytic expressions for the eigenvalues and eigenvectors of a vertically fractured system are presented, that have the same simplicity as those for transverse isotropy. New linearized expressions for mode‐converted amplitudes are developed for small angles of incidence and are used to interpret the synthetic response.



Elimination of source‐generated noise from correlated vibroseis data (the ‘ghost‐sweep’ problem)[Link]
By Ulrich PolomThe most common noise‐reduction methods employed in the vibroseis technique (e.g. spike and burst reduction, vertical stacking) are applied in the field to reduce noise at a very early stage. In addition, vibrator phase control systems prevent signal distortions produced by non‐linearity of the source itself. However, the success of these automatic correction methods depends on parameter justification by the operator and the actual characteristics of the distorting noise. More specific noise‐reduction methods (e.g. Combisweep (Trade mark of Geco‐Prakla), elimination of harmonics) increase production costs or need uncorrelated data for the correction process. Because the field data are usually correlated and vertically stacked in the field to minimize logistical and processing costs, it is not possible to make subsequent parameter corrections to optimize the noise reduction after correlation and vertical stacking of a production record.
The noise‐reduction method described here uses the final recorded, correlated and stacked vibroseis field data. This method eliminates signal artifacts caused e.g. by incorrect vibroseis source signals being used in parameter estimation when a frequency–time analysis is combined with a standard convolution process. Depending on the nature of the distortions, a synthetically generated, nearly recursive noise‐separation operator compresses the noise artifact in time using a trace‐by‐trace filter. After elimination of this compressed noise, re‐application of the separation operator leads to a noise‐corrected replacement of the input data. The method is applied to a synthetic data set and to a real vibroseis field record from deep seismic sounding, with good results.



Predicting horizontal velocities from well data[Link]
Authors M. Andrea, M.S. Sams, M.H. Worthington and M.S. KingThe Imperial College borehole test site consists of four boreholes with depths lying between 260 and 280 m. The boreholes intersect several cyclical sequences of sandstones, mudstones and limestones. The formations are highly laminated and ultrasonic measurements on preserved core have shown that the mudstones are intrinsically anisotropic. Little or no anisotropy is associated with the sandstones and limestones. A scheme is proposed to predict synthetic vertical and horizontal P‐ and S‐wave logs. Combining (an)isotropic effective medium theories, the Gassmann equation and Backus averaging, the scheme extends previous sand‐shale models to transversely isotropic rock formations. The model assumes that the anisotropy is due to layering and due to the preferred horizontal orientation of the clay minerals, pores and cracks within the mudstones. The pores and cracks within the sandstones and limestones are randomly orientated. After fitting the model to the ultrasonic data to obtain the unknown parameters, the model successfully predicts the sonic log and the direct arrival times from a cross‐hole survey.



Marine seismic sources: QC of wavefield computation from near‐field pressure measurements[Link]
Authors A.M. Ziolkowski and R.G.K. JohnstonA commercial marine seismic survey has been completed with the wavefield from the n‐element (single guns and clusters) airgun array measured for every shot using an array of n + 2 near‐field hydrophones, n of which were required to determine the source wavefield, the remaining two providing a check on the computation. The source wavefield is critical to the determination of the seismic wavelet for the extraction of reflection coefficients from seismic reflection data and for tying the data to wells. The wavefield generated by the full array of interacting airguns can be considered to be the superposition of n spherical pressure waves, or notional source signatures, the n hydrophone measurements providing a set of n simultaneous equations for each shot. The solution of the equations for the notional source signatures requires three ingredients: the geometry of the gun ports and near‐field hydrophones; the sensitivity of each hydrophone recording channel; and the relative motion between the near‐field hydrophones and the bubbles emitted by the guns. The geometry was measured on the back deck using a tape measure. A calibration data set was obtained at the approach to each line, in which each gun was fired on its own and the resulting wavefield was measured with the near‐field hydrophones and recorded. The channel sensitivities, or conversion from pressure at the hydrophones to numbers on the tape, were found for each near‐field hydrophone channel using the single gun calibration data, the measured geometry, and the peak pressure from each gun, known from the manufacturer’s calibration. The relative motion between the guns and hydrophones was obtained from the same calibration data set by minimizing the energy in the computed notional source signatures at the guns which did not fire. The full array data were then solved for the notional source signatures, and the pressure was computed at the two spare hydrophones and compared with the actual recordings. The rms errors were 5.3% and 2.8% and would have been smaller if the hydrophone channel sensitivities had been properly calibrated beforehand and if the movement of the guns with respect to the hydrophones had been more restricted. This comparison of the predicted and measured signatures at spare hydrophones can, in principle, be done on every shot and we recommend that this be implemented as a standard quality control procedure whenever it is desired to measure the wavefield of a marine seismic source.



Seismic migration and velocity analysis[Link]
More LessMigration using an erroneous velocity gives a curve along which the energy is smeared. Associated with this curve is the caustic enveloped by the normal rays. It is possible to compensate for an erroneous velocity by a simple modification of the imaging principle. Formulae are derived for the general case when the velocity changes laterally, and the position of the caustic suggests how to modify the imaging principle so as to obtain an estimate of the NMO velocity. A synthetic example is used to illustrate the results of the analysis.



Introduction to ground surface self‐potential tomography[Link]
More LessA new approach to self‐potential (SP) data interpretation for the recognition of a buried causative SP source system is presented. The general model considered is characterized by the presence of primary electric sources or sinks, located within any complex resistivity structure with a flat air‐earth boundary. First, using physical considerations of the nature of the electric potential generated by any arbitrary distribution of primary source charges and the related secondary induced charges over the buried resistivity discontinuity planes, a general formula is derived for the potential and the electric field component along any fixed direction on the ground surface. The total effect is written as a sum of elementary contributions, all of the same simple mathematical form. It is then demonstrated that the total electric power associated with the standing natural electric field component can be written in the space domain as a sum of cross‐correlation integrals between the observed component of the total electric field and the component of the field due to each single constitutive elementary charge. By means of the cross‐correlation bounding inequality, the concept of a scanning function is introduced as the key to the new interpretation procedure. In the space domain, the scanning function is the unit strength electric field component generated by an elementary positive charge. Next, the concept of charge occurrence probability is introduced as a suitable function for the tomographic imaging of the charge distribution geometry underground. This function is defined as the cross‐correlation product of the total observed electric field component and the scanning function, divided by the square root of the product of the respective variances. Using this physical scheme, the tomographic procedure is described. It consists of scanning the section, through any SP survey profile, by the unit strength elementary charge, which is given a regular grid of space coordinates within the section, at each point of which the charge occurrence probability function is calculated. The complete set of calculated grid values can be used to draw contour lines in order to single out the zones of highest probability of concentrations of polarized, primary and secondary electric charges. An extension to the wavenumber domain and to three‐dimensional tomography is also presented and discussed. A few simple synthetic examples are given to demonstrate the resolution power of the new SP inversion procedure.



Anisotropic migration of coincident VSP and cross‐hole seismic reflection surveys
More LessSeismic depth migration may result in false reflector positioning and destructive interference when an incorrect velocity field is used to convert from time to depth. The assumption of isotropy to describe anisotropic rocks is one major source of error in the velocity model, although individual survey images may not be impaired by such an approximation. When different survey types such as VSP and cross‐hole reflection seismics have coincident illumination of the subsurface, it is important not only to produce consistent images upon depth migration, but also to determine a consistent velocity model. Using real data sets as examples, both objectives are successfully achieved when anisotropy is incorporated into the velocity model.



3D targeted multiple attenuation[Link]
More LessShort‐period multiple reflections pose a particular problem in the North Sea where predictive deconvolution is often only partially successful. The targeted multiple attenuation (TMA) algorithm comprises computation of the covariance matrix of preflattened prestack or post‐stack seismic data, the determination of the dominating eigenvectors of the covariance matrix, and subtraction of the related eigenimages followed by reverse flattening. The main assumption made is that the flattened multiple reflections may be represented by the first eigenimage(s) which implies that the spatial amplitude variations of primaries and associated multiples are similar. This assumption usually limits the method to short‐period multiple reflections. TMA is applicable post‐stack or prestack to common‐offset gathers. It is computationally fast, robust towards random noise, irregular geometry and spatial aliasing, and it preserves the amplitudes of primaries provided they are not parallel to the targeted multiples. Application of TMA to 3D wavefields is preferable because this allows a better discrimination between primaries and multiples. Real data examples show that the danger of partially removing primary energy can be reduced by improving the raw multiple model that is based on eigenimages, for example by prediction filtering.



Time‐depth relationships for multilayer depth conversion[Link]
More LessThe conversion of seismic time to depth through the use of analytical functions has been a common procedure in seismic work for many decades. With the exception of recent examples dealing with the linear function, none of the published time‐depth relationships corresponding to these functions is applicable to multilayer depth conversion. The present work redresses this situation. It presents formulae applicable to multilayer depth conversion for a large number of analytical functions. The derivation is based on a procedure generally similar to that presented by Japsen (1993). Most of the functions considered date back to a publication by Kaufman in 1953 and earlier publications. A number of other functions hitherto not known in the industry are also presented.

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